MSSL SOLARNET School MHD Waves. Stephane REGNIER Northumbria University

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1 MSSL SOLARNET School 2016 MHD Waves Stephane REGNIER Northumbria University

2 MSSL SOLARNET School Definition of a wave 2. The three MHD waves a. Linearized MHD equations b. Dispersion relation c. Properties 3. MHD waves in different geometries a. Rectangular slab b. Cylinder 4. Solar observations of MHD waves 1. Slow modes 2. Fast modes 3. Alfvén modes

3 Definition of a wave MSSL SOLARNET School 2016

4 MSSL SOLARNET School 2016 The case of an electromagnetic wave: - The electric field and magnetic field are perpendicular - The wave is propagating along the direction perpendicular to the electric and magnetic fields - The propagation speed (phase speed) is the speed of light c Fig. 1: basic description of an electromagnetic wave

5 MSSL SOLARNET School 2016 A wave is defined by - The components of the electric field (polarisation, Stokes parameters) - The components of the magnetic field - The direction of the propagation or wave number - The dispersion relation: relation between the wavenumber and the angular frequency (see dispersion diagram) - The phase and group speeds - The perturbation of the thermodynamic quantities

6 MSSL SOLARNET School 2016

7 MSSL SOLARNET School 2016

8 MSSL SOLARNET School 2016

9 MHD waves MSSL SOLARNET School 2016

10 MSSL SOLARNET School 2016 The MHD equations are Linearized MHD equations

11 Linearized MHD equations MSSL SOLARNET School 2016

12 Linearized MHD equations MSSL SOLARNET School 2016

13 Linearized MHD equations MSSL SOLARNET School 2016

14 Linearized MHD equations MSSL SOLARNET School 2016

15 Linearized MHD equations MSSL SOLARNET School 2016

16 Dispersion relations MSSL SOLARNET School 2016

17 Dispersion relations MSSL SOLARNET School 2016

18 Dispersion relations MSSL SOLARNET School 2016

19 MSSL SOLARNET School 2016

20 MSSL SOLARNET School 2016

21 Some Properties MSSL SOLARNET School 2016

22 MSSL SOLARNET School 2016 Some Properties Magnetoacoustic waves - Phase speed varying with the angle of propagation - Group speed varying with the angle of propagation - Fast mode efficient to transport energy - Fast mode may have phase speed equal to Alfvén speed

23 MHD waves in different geometry MSSL SOLARNET School 2016

24 MSSL SOLARNET School 2016 Slab and Tube Geometry Wave in a non-uniform plasma - Two media: internal and external - Jump in density, temperature, magnetic field - Discontinuity at the interface - Total pressure balance - See for instance the Joarder and Roberts model

25 MSSL SOLARNET School 2016 Tube Geometry Surface and body modes - Generation of surface modes - Cylindrical coordinates - Bessel functions - Imposing boundary conditions to fully determine the waves properties

26 MSSL SOLARNET School 2016 Tube Geometry Representation of magnetoacoustic modes: sausage, kink and flute

27 MSSL SOLARNET School 2016 Some Properties Magnetoacoustic waves have different modes: sausage and kink

28 MSSL SOLARNET School 2016 Tube Geometry Dispersion diagram for coronal loop (coronal values)

29 MSSL SOLARNET School 2016 Tube Geometry Dispersion diagram for photosphere/chromosphere

30 Observations of waves MSSL SOLARNET School 2016

31 Slow modes Slow modes observed in coronal loops

32 MSSL SOLARNET School 2016 Fast kink modes Examples of fast modes generated by external sources such as flares

33 MSSL SOLARNET School 2016

34 MSSL SOLARNET School 2016

35 MSSL SOLARNET School 2016

36 Alfvenic modes MSSL SOLARNET School 2016

37 MSSL SOLARNET School 2016 Why to study waves? - Ubiquitous in the solar atmosphere - Transport of energy - Coronal heating - Chromospheric heating (reflection and transmission of waves) - Magnetic reconnection - Flares Not only MHD waves but also electronic and ionic plasma waves

38 MSSL SOLARNET School 2016 Instabilities Stephane REGNIER Northumbria University

39 1. Perturbation theory 2. Kink instability 3. Rayleigh-Taylor instability 4. Kelvin-Helmholtz instability 5. Thermal instability 6. Interchange instability

40 Perturbation Theory

41 Perturbation Theory

42 Perturbation Theory

43 Kink Instability Instability of a twisted flux tube exceeding a threshold of twist

44 Kink Instability

45 Rayleigh-Taylor Instability Two media with different thermodynamic and magnetic properties. No flow along x. z x Two cases: - Two plasmas with a uniform magnetic field - One plasma supported by magnetic field

46 Rayleigh-Taylor Instability

47 Rayleigh-Taylor Instability

48 Rayleigh-Taylor Instability

49 Kelvin-Helmholtz Instability Hydrodynamic instability with two media with different flows

50

51

52 Kelvin-Helmholtz Instability

53 Thermal Instability

54 Thermal Instability

1. A tendency to roll or heel when turning (a known and typically constant disturbance) 2. Motion induced by surface waves of certain frequencies.

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